On a general Maclaurin's inequality
Authors:
Stefano Favaro and Stephen G. Walker
Journal:
Proc. Amer. Math. Soc. 146 (2018), 175-188
MSC (2010):
Primary 26D15, 26C05
DOI:
https://doi.org/10.1090/proc/13673
Published electronically:
July 20, 2017
Addendum:
Proc. Amer. Math. Soc. 146 (2018), 2217-2218.
MathSciNet review:
3723131
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Abstract | References | Similar Articles | Additional Information
Abstract: Maclaurin's inequality provides a sequence of inequalities that interpolate between the arithmetic mean at the high end and the geometric mean at the low end. We introduce a similar interpolating sequence of inequalities between the weighted arithmetic and geometric mean with arbitrary weights. Maclaurin's inequality arises for uniform weights. As a by-product we obtain inequalities that may be of interest in the theory of Jacobi polynomials.
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Additional Information
Stefano Favaro
Affiliation:
Department of Economics and Statistics, University of Torino, Corso Unione Sovietica 218/bis, 10134 Torino, Italy
Email:
stefano.favaro@unito.it
Stephen G. Walker
Affiliation:
Department of Mathematics, University of Texas at Austin, One University Station, C1200 Austin, Texas
Email:
s.g.walker@math.utexas.edu
DOI:
https://doi.org/10.1090/proc/13673
Received by editor(s):
July 11, 2016
Received by editor(s) in revised form:
January 22, 2017
Published electronically:
July 20, 2017
Communicated by:
Mourad E. H. Ismail
Article copyright:
© Copyright 2017
American Mathematical Society
